(8-3i)(-6-20i)=0

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Solution for (8-3i)(-6-20i)=0 equation: 


Simplifying
(8 + -3i)(-6 + -20i) = 0

Multiply (8 + -3i) * (-6 + -20i)
(8(-6 + -20i) + -3i * (-6 + -20i)) = 0
((-6 * 8 + -20i * 8) + -3i * (-6 + -20i)) = 0
((-48 + -160i) + -3i * (-6 + -20i)) = 0
(-48 + -160i + (-6 * -3i + -20i * -3i)) = 0
(-48 + -160i + (18i + 60i2)) = 0

Combine like terms: -160i + 18i = -142i
(-48 + -142i + 60i2) = 0

Solving
-48 + -142i + 60i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + -71i + 30i2) = 0

Factor a trinomial.
2((-3 + -10i)(8 + -3i)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + -10i)' equal to zero and attempt to solve:

Simplifying
-3 + -10i = 0

Solving
-3 + -10i = 0

Move all terms containing i to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -10i = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -10i = 0 + 3
-10i = 0 + 3

Combine like terms: 0 + 3 = 3
-10i = 3

Divide each side by '-10'.
i = -0.3

Simplifying
i = -0.3

Subproblem 2
Set the factor '(8 + -3i)' equal to zero and attempt to solve:

Simplifying
8 + -3i = 0

Solving
8 + -3i = 0

Move all terms containing i to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -3i = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3i = 0 + -8
-3i = 0 + -8

Combine like terms: 0 + -8 = -8
-3i = -8

Divide each side by '-3'.
i = 2.666666667

Simplifying
i = 2.666666667
Solution
i = {-0.3, 2.666666667}

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